First, the reason for using a house wrap is to provide a vapor barrier. You already have one.
If I were going to side your house, I would recomend you install 1/2" foil faced, 4' X 8' ridged insulation. Brand names that come to mind are "NRG" & "Energy Sheild". This should give you about a 3.6 R-Value on top of what you already have. (Oh, this is a vapor barrier too!)
If your salesperson is pushing, push him/her out the door!
A GOOD Home Improvement company has been around a long time and should have good word of mouth reputation in your community!
They should be able to provide you with a certificate of insurance so if a worker gets hurt on your property, you won't be paying the bill.
Get a contract that spells everything out! Brand names of everything you agree on and how long they stand behind their workmanship. When they plan to start and finish, (depending on the weather).
Payment schedule should be set up in such a mannor that you never get too far behind the contractor. I used to schedule, 1/3 down, 1/3 when half the job was done and the balance when done.
You should insist on a manufacturer like Certainteed/Wolverine or Alcoa/Mastic that will provide a lifetime warranty on the material. .044 is a good thickness.
Make sure you have the soffit(vinyl) and fascia (aluminum)covered and use the vinyl Gable vents, light blocks, and shutters.
I like to think of it like a woman who gets all dressed up and forgets the make up! (hope I did not offend anyone)